Sounds to me like you have a classic case of a laying worker.  Even newly
mated queens only lay one egg per cell, and in the center of the bottom.
In all my reading, what you have described is typically what a laying
worker does.
 
On Sat, 27 May 1995, David F. Verville wrote:
 
> Several weeks ago, I started to make a new queen by putting a couple
> of frames with eggs into a nuc box.
> Two weeks ago I saw what I thought was the queen but she hadn't started
> to lay yet. All of the brood had emerged.
> Today at hign noon, with no smoke, I openned it again,  (4X)
> I did not see the queen but I did see eggs and some other STRANGE things!
> First I should say that the bees were very content! (Red pollen again!)
>
> 1 There were three queen cells with two and three eggs inside.
> 2 There were some cells with two or three eggs inside.
> 3 There were cells with eggs attached to the very bottom but at the sides.
>   Some eggs where not at the bottom but half way up an the sides.
> 4 There were many many cells where the egg was perfectly
>   centered as they should be.
> 5 There where eggs outside the pollen/honey band.
>
> I am assuming that there is a mated queen, she just has not got her act
> together or shall I assume a laying worker.
> I guess I will really know a week from now as the cells get capped.
> Any one ever see this before?
> Dave Verville
>
> att!mvtowers!mvdfv
>